Integration formulas
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22 Terms
1
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∫ dx
= x + C
2
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∫ xʳ dx
= (xʳ⁺¹) / (r + 1) + C (r ≠ -1)
3
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∫ cos x dx
sin x + C
4
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∫ sin x dx
= -cos x + C
5
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∫ sec² x dx
= tan x + C
6
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∫ csc² x dx
= -cot x + C
7
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∫ sec x tan x dx
= sec x + C
8
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∫ csc x cot x dx
= -csc x + C
9
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∫ eˣ dx
= eˣ + C
10
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∫ bˣ dx
= (bˣ) / ln b + C (0 < b, b ≠ 1)
11
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∫ (1 / x) dx
= ln |x| + C
12
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∫ (1 / (1 + x²)) dx
= tan⁻¹ x + C
13
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∫ (1 / √(1 - x²)) dx
= sin⁻¹ x + C
14
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∫ (1 / (x√(x² - 1))) dx
= sec⁻¹ |x| + C
15
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∫ c f(x) dx
= c ∫ f(x) dx
16
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∫ [f(x) + g(x)] dx
= ∫ f(x) dx + ∫ g(x) dx
17
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∫ [f(x) - g(x)] dx
= ∫ f(x) dx - ∫ g(x) dx
18
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tan(x)=
Sine X over cosine X
19
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csc(x)=
One over sine x
20
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sec(x)=
One over cosine X
21
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Cot x =
Cosine x over sine x
22
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cos²(x) + sin²(x)=
1